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nil))
nil)
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nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil))
nil))
(sq_neg_pos_lt 0
(sq_neg_pos_lt-1 nil 3255279994
("" (skolem 1 ("a" "c"))
(("" (case "a >= 0")
(("1" (lemma "sq_lt")
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("2" (lemma "sq_lt")
(("2" (inst -1 "-a" "c")
(("1" (case-replace "sq(-a) = sq(a)")
(("1" (ground) nil nil)
("2" (hide -1 3)
(("2" (expand "sq") (("2" (assert) nil nil)) nil)) nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil)
((>= const-decl "bool" reals nil)
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(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(a skolem-const-decl "real" sq nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(sq_lt formula-decl nil sq nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(real_times_real_is_real application-judgement "real" reals nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(sq const-decl "nonneg_real" sq nil))
nil))
(neg_pos_sq_lt 0
(neg_pos_sq_lt-1 nil 3255279994
("" (skolem 1 ("a" "b"))
(("" (ground)
(("" (case "a > 0")
(("1" (lemma "sq_lt")
(("1" (inst -1 "a" "b")
(("1" (ground) nil nil) ("2" (ground) nil nil)) nil))
nil)
("2" (case "-a < b")
(("1" (lemma "sq_lt")
(("1" (inst -1 "-a" "b")
(("1" (ground) (("1" (rewrite "sq_neg") nil nil)) nil)
("2" (ground) nil nil))
nil))
nil)
("2" (ground) nil nil))
nil))
nil))
nil))
nil)
((real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(minus_real_is_real application-judgement "real" reals nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(< const-decl "bool" reals nil) (sq_neg formula-decl nil sq nil)
(sq_lt formula-decl nil sq nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(a skolem-const-decl "real" sq nil)
(>= const-decl "bool" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(> const-decl "bool" reals nil))
nil))
(sq_le_abs 0
(sq_le_abs-1 nil 3255279994
("" (skosimp*)
(("" (case-replace "b!1 >= 0")
(("1" (lemma "sq_neg_pos_le")
(("1" (inst?)
(("1" (expand "abs")
(("1" (lift-if) (("1" (ground) nil nil)) nil)) nil))
nil))
nil)
("2" (lemma "sq_neg_pos_le")
(("2" (inst -1 "a!1" "-b!1")
(("1" (case-replace "sq(-b!1) = sq(b!1)")
(("1" (hide -1)
(("1" (expand "abs")
(("1" (lift-if) (("1" (ground) nil nil)) nil)) nil))
nil)
("2" (hide -1 3)
(("2" (expand "sq") (("2" (assert) nil nil)) nil)) nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil)
((number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
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(b!1 skolem-const-decl "real" sq nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(sq_neg_pos_le formula-decl nil sq nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(real_times_real_is_real application-judgement "real" reals nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(sq const-decl "nonneg_real" sq nil))
nil))
(sq_lt_abs 0
(sq_lt_abs-1 nil 3255279994
("" (skosimp*)
(("" (case-replace "b!1 >= 0")
(("1" (lemma "sq_neg_pos_lt")
(("1" (inst?)
(("1" (expand "abs")
(("1" (lift-if) (("1" (ground) nil nil)) nil)) nil))
nil))
nil)
("2" (lemma "sq_neg_pos_lt")
(("2" (inst -1 "a!1" "-b!1")
(("1" (case-replace "sq(-b!1) = sq(b!1)")
(("1" (hide -1)
(("1" (expand "abs")
(("1" (lift-if) (("1" (ground) nil nil)) nil)) nil))
nil)
("2" (hide -1 3)
(("2" (expand "sq") (("2" (assert) nil nil)) nil)) nil))
nil)
("2" (assert) nil nil))
nil))
nil))
nil))
nil)
((number nonempty-type-decl nil numbers nil)
(boolean nonempty-type-decl nil booleans nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(real nonempty-type-from-decl nil reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(b!1 skolem-const-decl "real" sq nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(minus_real_is_real application-judgement "real" reals nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(sq_neg_pos_lt formula-decl nil sq nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(real_times_real_is_real application-judgement "real" reals nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(sq const-decl "nonneg_real" sq nil))
nil))
(sq_ge_abs 0
(sq_ge_abs-1 nil 3256039469
("" (skosimp*)
(("" (lemma "sq_le_abs")
(("" (inst -1 "b!1" "a!1") (("" (ground) nil nil)) nil)) nil))
nil)
((sq_le_abs formula-decl nil sq nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
nil))
(sq_gt_abs 0
(sq_gt_abs-1 nil 3256039548
("" (skosimp*)
(("" (lemma "sq_lt_abs")
(("" (inst -1 "b!1" "a!1")
(("" (assert) (("" (ground) nil nil)) nil)) nil))
nil))
nil)
((sq_lt_abs formula-decl nil sq nil)
(real_gt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
shostak))
(sq_eq_abs 0
(sq_eq_abs-1 nil 3255279994
("" (skosimp*)
(("" (case "a!1 >= 0")
(("1" (case "b!1 >= 0")
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("2" (case-replace "sq(b!1) = sq(-b!1)")
(("1" (hide -1)
(("1" (rewrite "sq_eq") (("1" (grind) nil nil)) nil)) nil)
("2" (hide 3)
(("2" (expand "sq") (("2" (assert) nil nil)) nil)) nil))
nil))
nil)
("2" (case "b!1 >= 0")
(("1" (case-replace "sq(a!1) = sq(-a!1)")
(("1" (hide -1)
(("1" (rewrite "sq_eq") (("1" (grind) nil nil)) nil)) nil)
("2" (hide 3)
(("2" (expand "sq") (("2" (assert) nil nil)) nil)) nil))
nil)
("2" (case-replace "sq(a!1) = sq(-a!1)")
(("1" (case-replace "sq(b!1) = sq(-b!1)")
(("1" (hide -1 -2)
(("1" (rewrite "sq_eq") (("1" (grind) nil nil)) nil))
nil)
("2" (hide -1 4)
(("2" (expand "sq") (("2" (assert) nil nil)) nil)) nil))
nil)
("2" (hide 4)
(("2" (expand "sq") (("2" (assert) nil nil)) nil)) nil))
nil))
nil))
nil))
nil)
((>= const-decl "bool" reals nil)
(bool nonempty-type-eq-decl nil booleans nil)
(real nonempty-type-from-decl nil reals nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil)
(minus_real_is_real application-judgement "real" reals nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(sq const-decl "nonneg_real" sq nil)
(numfield nonempty-type-eq-decl nil number_fields nil)
(- const-decl "[numfield -> numfield]" number_fields nil)
(real_times_real_is_real application-judgement "real" reals nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq_eq formula-decl nil sq nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
(abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
nil)
(real_lt_is_strict_total_order name-judgement
"(strict_total_order?[real])" real_props nil))
nil))
(sq_eq_rew 0
(sq_eq_rew-1 nil 3409051947
("" (skosimp*) (("" (assert) nil nil)) nil) nil shostak))
(triangle_rectangle 0
(triangle_rectangle-1 nil 3255279994
("" (skolem 1 ("a" "b" "c"))
(("" (flatten)
(("" (case "sq(a)>=0" "sq(b)>=0" "sq(c)>=0")
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(("1" (case "sq(b) <= sq(c)")
(("1" (lemma "sq_neg_pos_le")
(("1" (inst-cp -1 "a" "c")
(("1" (inst -1 "b" "c") (("1" (ground) nil nil)) nil))
nil))
nil)
("2" (hide 2 -1) (("2" (ground) nil nil)) nil))
nil)
("2" (hide 2 -1) (("2" (ground) nil nil)) nil))
nil)
("2" (rewrite "sq_pos") nil nil)
("3" (rewrite "sq_pos") nil nil)
("4" (rewrite "sq_pos") nil nil))
nil))
nil))
nil)
((sq_pos formula-decl nil sq nil) (<= const-decl "bool" reals nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(real_ge_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
(sq_neg_pos_le formula-decl nil sq nil)
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(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(number_field nonempty-type-from-decl nil number_fields nil)
(real_pred const-decl "[number_field -> boolean]" reals nil)
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(bool nonempty-type-eq-decl nil booleans nil)
(>= const-decl "bool" reals nil)
(nonneg_real nonempty-type-eq-decl nil real_types nil)
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nil))
(triangle_ineq_lt 0
(triangle_ineq_lt-1 nil 3255279994
("" (skosimp*)
(("" (lemma "sq_lt_abs")
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(("" (lemma "sq_lt_abs")
(("" (inst -1 "b!1" "d!1") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((sq_lt_abs formula-decl nil sq nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
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(real nonempty-type-from-decl nil reals nil)
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(number_field nonempty-type-from-decl nil number_fields nil)
(number_field_pred const-decl "[number -> boolean]" number_fields
nil)
(boolean nonempty-type-decl nil booleans nil)
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nil))
(triangle_ineq_le 0
(triangle_ineq_le-1 nil 3255279994
("" (skosimp*)
(("" (lemma "sq_le_abs")
(("" (inst?)
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(("" (lemma "sq_le_abs")
(("" (inst -1 "b!1" "d!1") (("" (assert) nil nil)) nil))
nil))
nil))
nil))
nil))
nil)
((sq_le_abs formula-decl nil sq nil)
(nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
real_types nil)
(real_le_is_total_order name-judgement "(total_order?[real])"
real_props nil)
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(real_pred const-decl "[number_field -> boolean]" reals nil)
(number_field nonempty-type-from-decl nil number_fields nil)
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nil)
(boolean nonempty-type-decl nil booleans nil)
(number nonempty-type-decl nil numbers nil))
nil)))
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Entwicklung einer Software für die statische Quellcodeanalyse
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